Symmetry-Preserving Finite Element Schemes: An Introductory Investigation

DOI10.1137/18M1177524zbMath1436.65092arXiv1803.10058OpenAlexW2982010694WikidataQ126991885 ScholiaQ126991885MaRDI QIDQ5241269

Alexander Bihlo, Francis Valiquette

Publication date: 30 October 2019

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1803.10058

zbMATH Keywords

finite elementsordinary differential equationsgeometric numerical integrationmoving framesinvariant discretization

Mathematics Subject Classification ID

Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Numerical methods for initial value problems involving ordinary differential equations (65L05) Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations (65L60) Numerical methods for Hamiltonian systems including symplectic integrators (65P10)

Related Items

Invariant variational schemes for ordinary differential equations ⋮ On the development of symmetry-preserving finite element schemes for ordinary differential equations

Cites Work

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• Convecting reference frames and invariant numerical models
• Adaptive moving mesh methods
• Transformation groups in network spaces
• Structure preserving discretizations of the Liouville equation and their numerical tests
• Moving coframes. II: Regularization and theoretical foundations
• Lie point symmetry preserving discretizations for variable coefficient Korteweg-de Vries equations
• Symmetry and integration methods for differential equations
• Discrete moving frames on lattice varieties and lattice-based multispaces
• Geometric integration via multi-space
• Lie-Poisson Hamilton-Jacobi theory and Lie-Poisson integrators
• Invariant discretization schemes using evolution-projection techniques
• Invariantization of the Crank-Nicolson method for Burgers' equation
• Lie group classification of second-order ordinary difference equations
• Symmetry-adapted moving mesh schemes for the nonlinear Schrödinger equation
• A Concise Introduction to Geometric Numerical Integration
• Symmetry preserving discretization of ordinary differential equations. Large symmetry groups and higher order equations
• Simulating Hamiltonian Dynamics
• The Multiplier Method to Construct Conservative Finite Difference Schemes for Ordinary and Partial Differential Equations
• Symmetry-preserving difference schemes for some heat transfer equations
• Invariant Discretization Schemes for the Shallow-Water Equations
• Invariant meshless discretization schemes
• The Korteweg–de Vries equation and its symmetry-preserving discretization
• Symmetry preserving numerical schemes for partial differential equations and their numerical tests
• Symmetry Preserving Discretization of SL(2,R) Invariant Equations
• Symmetry-Preserving Numerical Schemes
• Conservative Methods for Dynamical Systems
• A new class of energy-preserving numerical integration methods
• Geometric Numerical Integration
• Difference schemes with point symmetries and their numerical tests
• The nonlinear differential equation 𝑦”+𝑝(𝑥)𝑦+𝑐𝑦⁻³=0
• Geometric foundations of numerical algorithms and symmetry